Scanning electron microscopy and molecular dynamics of ice surfaces: What is the origin of trans-prismatic strands?

1. IntroductionClimatologically significant optical properties of atmospheric ice crystals depend not only on crystal habit but also on mesoscopic (μm-level) surface properties1. Variable-pressure scanning electron microscopy (VPSEM) observations of growing and ablating hexagonal ice crystals have revealed mesoscopic surface features associated with low supersaturation and ablation, called trans-prismatic strands2 (Figs. 1-3). Using a combination of VPSEM experiments and molecular dynamics (MD) simulations of the ice-vapor interface, we explore possible factors influencing these features.

AcknowledgementsThis research was supported by the Czech Science Foundation (grant no. P208/10/1724), the Ministry of Education of the Czech Republic (grant no. ME09064), and the University of Puget Sound. We thank Babak Minofar and Morteza Khabiri for technical assistance related to MD, and Al Vallecorsa for technical assistance related to VPSEM. We would especially like to acknowledge Victoria Buch for her generosity in various respects: in providing computer code that generated proton-disordered ice configurations, and in listening carefully and sharing her insights during many fruitful discussions about liquid water and ice.

Steven Neshyba1*, Will Pfalzgraff1,2, and Martina Roeselova2

1University of Puget Sound, Tacoma, WA

2Institute of Organic Chemistry and Biochemistry, Prague, Czech Republic.

*nesh@pugetsound.edu

2. Methods1. VPSEM. The chamber of a Hitachi S-3400N variable-

pressure scanning electron microscope equipped with a backscatter detector was humidified with a liquid or ice reservoir, resulting in ice crystal formation on a cold stage (Fig. 4). Growth and ablation were controlled by adjusting the temperature of the cold stage (nominal Tmin = -50°C).

2. MD. Slabs consisting of 2880 rigid water molecules, interacting via the NE6 intermolecular potential3 at T=250K (~40°C below the NE6 melting temperature4), were allowed to evolve classically using Gromacs5 molecular dynamics software. The prismatic slab, created using a proton-disordering algorithm6, measured 5.4, 4.7, and 3.7 nm (in the x-, y-, and z-directions). The simulation box was extended in the y-direction to simulate exposure of the prismatic surface to vacuum. The pyramidal slab was structured similarly, but rotated 28° along the x-axis, with rectangular periodic boundary conditions adjusted accordingly (Fig. 5). The resulting slab measured 5.4, 4.1, and 4.2 nm (in the x-, y’-, and z’-directions). The simulation box was extended in the y’-direction to simulate exposure of the pyramidal surface to vacuum. Fig. 6 shows densities of oxygen atoms normal to exposed facets of each slab. Degradation of peaks at the extremes indicates quasiliquid layer (QLL) formation.

References1. Garrett, in Light Scattering Reviews, 2008 (edited by Kokhanovsky).2. Pfalzgraff, Hulscher, & Neshyba, Atmospheric Chemistry and Physics, 2010, 10, 2927-2935.3. Nada & van der Eerden, The Journal of Chemical Physics 2003, 118, 7401.4. Abascal et al, The Journal of Chemical Physics 2006, 125, 166101.5. Lindahl et al, Journal of Molecular Modeling 2001, 7, 306-317.6. Buch, Sandler, P& Sadlej, J. Phys. Chem. B 1998, 102, 8641-8653.7. Neshyba, Nugent, Roeselova, & Jungwirth, J. Phys. Chem. C, 2009, 113, 4597-4604.8. Bales & Zangwill, Phys. Rev. B., 1989, 41, 5500-5508.9. Burton, Cabrera, & Frank, Philos. Trans. R. Soc. London, Ser. A., 1951, 243, 299-358.

Fig. 7. Three unit cells of a 1280-molecule slab in which upper and lower basal surfaces are exposed to vacuum, a few picoseconds after a sublimation event (from ref. 7).

Fig. 3. Mesoscopic trans-prismatic strands associated with growth (A; C-F) and ablation (B; G-I) (from ref. 2).

3. Insights from MD1. Thermodynamics. Previous MD simulations of ice slabs at 250K with basal surfaces exposed to vacuum7

exhibited a sublimation rate equivalent to Pvap ≈ 230 Pa (Fig. 7). To explore whether thermodynamic stability (using equilibrium vapor pressure as a proxy for chemical potential) influences mesoscopic structuring, we carried out sublimation studies of prismatic and pyramidal facets. Simulations over 200 ns revealed sublimation rates identical to that of basal surfaces, to two significant figures. Conclusions: The chemical potential of facet surfaces is probably washed out by the QLL at 250K. Moreover, since all surfaces are likely to be QLL-covered at this temperature, we infer that thermodynamic considerations do not influence structure at the mesoscopic level.

2. Sublayer nucleation dynamics. We observed growth in our VPSEM experiments as fast as 1 μm/s, which corresponds to ~10 -6 layers/ns; observed mesoscopic structures appear to develop on an even slower time scale (seconds). To investigate whether such structuring could be influenced by layer nucleation, we carried out MD simulations at 250K of the prismatic and pyramidal slabs modified such that a second QLL was inserted under the existing one, producing a “doubled QLL” (Fig. 8). It was found that doubled-QLLs re-freeze after ~5 ns (0.2 layers/ns) (Fig. 9), with prismatic slightly faster. Conclusion: Sublayer nucleation occurs on a time scale that is fast enough to influence observed mesoscopic structuring. If such is the case, it follows that differences between prismatic and pyramidal freezing rates may play a significant role in influencing mesoscopic structure.

Fig. 8. Doubled-QLL MD experiment for a prismatic facet. (a) 2880-molecule prismatic slab with fully developed upper and lower QLLs. (b) Displaced upper QLL replaces the underlying ice layer. (c) Layers coalesced into a doubled-QLL a few picoseconds later. (d) QLL restoration after 5 ns.

Fig. 9. Potential energy curves of doubled-QLL simulations, for 2880-molecule prismatic and pyramidal slabs. Multiple runs correspond to slightly different initial configurations of the doubled-QLL. Green curves indicate the mean +/- 1 standard deviation of potential energies of unperturbed slabs.

3. Surface diffusion dynamics. Mesoscopic structure seen on prismatic facets of VPSEM-grown ice exhibits strong directional preference. Under conditions near the frost point, surface growth appears to be morphologicaly unstable (see Figs. 2 & 3). To investigate whether such preference could be influenced by surface diffusion, we used MD to evaluate the root-mean-square displacement of surface molecules (Figs. 10 & 11). Diffusion of molecules on the prismatic facet is found to be anisotropic (Dx>Dz), i.e., trans-prismatic diffusion is faster than basal-to-basal diffusion. Analogous behavior is observed for diffusion of molecules on the pyramidal facet (D x>Dz’), although the anisotropy is smaller. Conclusion: Anisotropic diffusivity is a plausible cause of the geometrical and dynamical asymmetry observed of trans-prismatic strands in VPSEM experiments, perhaps via a mechanism analogous to the morphological instability of terrace edges in step flow 8,9.

Fig. 10. MD simulation showing displacement of QLL molecules in the z’ (basal-to-basal) direction of a pyramidal slab after 10 ns simulated time.

Fig. 11. MD-derived mean-squared displacement of QLL molecules in prismatic and pyramidal slabs, assuming ice:QLL ratios of 10:2 for the prismatic slab and 9:3 for the pyramidal slab (see Fig. 6). Diffusion coefficients are one-dimensional, in units 10-5 cm2/s. Coordinates are as specified in Fig. 5.

Fig. 6. Oxygen atom densities as a function of distance along the surface normal of 2880-molecule prismatic and pyramidal slabs. Each outer layer of the prismatic slab is designated quasiliquid (QLL); each 1½ outer layer of the pyramidal slab is designated QLL.

Fig. 1. Facets observed in VPSEM-grown ice crystals, designated here as basal (0001), prismatic (1010), and pyramidal (1011) (from ref. 2).

Fig. 5. Coordinate systems for prismatic and pyramidal slabs.

Fig. 4. Hitachi S-3400NVPSEM chamber with Peltier cooler.

Fig. 2. Evidence of ledge growth instability on prismatic facets.

(a)

(b)

(c)

(d)~10 ps

~5 ns